Question

Two carnivals charge different amounts for each ride and to go inside.

Carnival M charges an entrance fee of $5.00 and $0.65 per ticket for the rides.
Carnival P charges an entrance fee of $10.00 and $0.45 per ticket for the rides.
Which inequality can be used to find x, the number of tickets Carnival M needs to sell so that the total amount charged is greater than Carnival P?

A) 0.65x + 10 > 0.45x + 5
B) 5x > 10 - 0.45x
C) 5 + 0.65x < 10 + 0.45x
D) 0.653x + 5 > 0.453x + 10

Answer 1

To determine the number of tickets Carnival M needs to sell so that its total amount charged is greater than Carnival P, the correct inequality is 0.65x + 5 > 0.45x + 10. This inequality correctly accounts for the entrance fees and per-ticket costs for both carnivals.

Step-by-step explanation:

The question involves setting up an inequality to compare the total costs of tickets and entrance fees for two carnivals, specifically to find x, the number of tickets Carnival M needs to sell so that its total amount charged is greater than that of Carnival P. The correct inequality for this situation should account for the entrance fee and per-ticket cost of both carnivals.

Let's analyze the options provided:

• Option A) 0.65x + 10 > 0.45x + 5 incorporates both entrance fees and per-ticket costs for carnivals M and P respectively. However, it incorrectly attributes Carnival P's entrance fee to Carnival M.
• Option B) 5x > 10 - 0.45x compares the entrance fees, but not in the per-ticket price context.
• Option C) 5 + 0.65x < 10 + 0.45x is the inequality in the wrong direction. We want Carnival M's total to be greater, not lesser.
• Option D) 0.65x + 5 > 0.45x + 10 is the correct inequality. It includes the entrance fee of Carnival M and the cost per ticket for both carnivals. Carnival M's total cost will be greater than Carnival P's if this inequality holds true.

So, the correct inequality is:

0.65x + 5 > 0.45x + 10